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<p>Ultrasonic shot peening (USP) is an advanced cold working technology increasingly applied for mode-free, flexible forming of metal sheets. This study aims to investigate the effects of sheet thickness and USP duration on the bulging deformation behavior of 2024 aluminum alloy sheets. A series of USP-induced metal sheet bulging experiments were conducted to investigate the deformation behaviors. Results revealed a transition in the USP-deformed sheet shape from spherical to cylindrical with the increase in USP duration or decrease in sheet thickness, attributed to the elastic deformation instability induced by USP. Based on experimental measurements, the rational fitting method (RFM) and response surface method (RSM) were employed to predict the arc heights of USP-deformed metal sheets, respectively. For the arc heights along the length direction, the fitting parameters in RFM and RSM were determined at the coefficient of determination (<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40430_2025_5819_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\(R^{2}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>R</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation>) larger than 99.4% and root mean squared error (RMSE) smaller than 2.5%. However, for the arc heights along the width direction, which increases first, then decreases, and then increases again with the increase in USP duration due to elastic instability, the fitting parameters in RFM and RSM were determined at <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40430_2025_5819_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\(R^{2}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>R</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation> of 88.8 and 91.75%, and RMSE of 7.5 and 4.8%, respectively. To confirm the statistical agreement between numerically-predicted and experimentally-measured arc heights, two-sample t-tests were performed. No significant differences were found: the values of <i>p</i> are 0.688 for RSM prediction and 0.7844 for RFM prediction in the case of the length direction; and 0.1261 (RSM) and 0.206 (RFM) for the width direction. These results validate the reliability of both methods in predicting USP-induced metal sheet bulging deformation, taking into account cases affected by elastic instability. This work provides a fast and cost-effective approach for predicting and evaluating USP-induced metal sheet bulging deformation.</p>

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On metal sheet bulging deformation induced by ultrasonic shot peening

  • 期刊论文

  • 发表日期：

    2025年8月8日

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  • Kaixiang Chang,
  • Shuhui Fei,
  • Cheng Xu,
  • Senhui Wang,
  • Cheng Wang

摘要

Ultrasonic shot peening (USP) is an advanced cold working technology increasingly applied for mode-free, flexible forming of metal sheets. This study aims to investigate the effects of sheet thickness and USP duration on the bulging deformation behavior of 2024 aluminum alloy sheets. A series of USP-induced metal sheet bulging experiments were conducted to investigate the deformation behaviors. Results revealed a transition in the USP-deformed sheet shape from spherical to cylindrical with the increase in USP duration or decrease in sheet thickness, attributed to the elastic deformation instability induced by USP. Based on experimental measurements, the rational fitting method (RFM) and response surface method (RSM) were employed to predict the arc heights of USP-deformed metal sheets, respectively. For the arc heights along the length direction, the fitting parameters in RFM and RSM were determined at the coefficient of determination ( \(R^{2}\) R 2 ) larger than 99.4% and root mean squared error (RMSE) smaller than 2.5%. However, for the arc heights along the width direction, which increases first, then decreases, and then increases again with the increase in USP duration due to elastic instability, the fitting parameters in RFM and RSM were determined at \(R^{2}\) R 2 of 88.8 and 91.75%, and RMSE of 7.5 and 4.8%, respectively. To confirm the statistical agreement between numerically-predicted and experimentally-measured arc heights, two-sample t-tests were performed. No significant differences were found: the values of p are 0.688 for RSM prediction and 0.7844 for RFM prediction in the case of the length direction; and 0.1261 (RSM) and 0.206 (RFM) for the width direction. These results validate the reliability of both methods in predicting USP-induced metal sheet bulging deformation, taking into account cases affected by elastic instability. This work provides a fast and cost-effective approach for predicting and evaluating USP-induced metal sheet bulging deformation.